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215anotes_final

215anotes_final - EE215A Fall 08 B Razavi HO#11 Why Analog...

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EE215A B. Razavi Fall 08 HO #11 Why Analog? - Naturally-occurring signals, e.g., voice and video, are analog. - System and medium non-idealities often make it necessary to treat digital signals as analog: o Data Retrieved from Disk o Digital Wireless Communications Why is analog design such a big deal? - Entails more trade-offs than digital design: Digital Analog speed power speed power - More sensitive to noise and cross-talk. - More sensitive to second-order effects in devices. - More difficult to automate. - More difficult to model and simulate. - We want to design analog circuits in mainstream VLSI technologies, e.g., CMOS, with no additional processing steps, trimming, factory calibration, etc. 1
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EE215A B. Razavi Fall 08 HO #11 REVIEW OF MOS DEVICES MOS Structure (NMOS) - A piece of polysilicon with a width of W and length of L on top of a thin layer of oxide defines the gate area. - Source and drain areas are heavily doped. - Substrate usually tied to the most negative voltage. - Le ff = L – 2L D , where L D is the side diffusion of source and drain. MOS Symbols (Enhancement Type) PMOS NMOS - MOS structure is symmetric. - MOS devices have a very high input impedance. 2
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EE215A B. Razavi Fall 08 HO #11 MOS characteristics o How does the device turn on and off? o What is the drain-source current when the device is on? Threshold Voltage For V GS < V TH , holes in substrate are repelled from gate area, leaving negative ions behind. (No current flows because no carriers are available.) A depletion region forms under the gate. For V GS ≈ V TH , electrons are attracted to the interface under gate, establishing a “channel” for conduction. The channel is also called the “inversion layer.” For V GS ≈ V TH , depletion region under channel remains relatively constant, but the charge in inversion layer increases . Turn-on process not really abrupt, i.e., for V GS ≈ V TH , I D > o. => Sub- threshold conduction (considered later). For a long-channel device with uniform substrate doping: (and V sub = V source ): 3
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EE215A B. Razavi Fall 08 HO #11 where Often need to implant the channel to obtain the “right” threshold. A helpful approximation: For V GS ≈ V TH , there is only depletion region in the gate area; for V GS ≈ V TH , the depletion region is constant and the inversion layer charge increases. A useful Lemma: If a conductor carries a constant current I and it has a charge density (charge per unit length ) of Q d and the charge moves with a velocity v: I = Q d v MOS I – V Characteristics For V DS > o, the inversion layer charge is non-uniform: 4
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EE215A B. Razavi Fall 08 HO #11 Note that as we approach the end of the channel, the charge density falls. To find the current, multiply charge density by charge velocity. For a semiconductor: The drain current is therefore given by subject to boundary conditions at the two ends of the channel. Thus, and hence, Assumptions made: 1. One-dimensional structure 2. Constant mobility 3.
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